Santos Ltd. of Australia rejected a more than US$10 billion acquisition offer by Harbour Energy Ltd. on Tuesday, saying the offer undervalued it given recent oil-price gains.

The rejection comes after private-equity-backed Harbour—set up by EIG Global Energy Partners in 2014 to hunt for oil and natural-gas assets outside the U.S.—raised its offer twice in recent days to woo Santos. The latest proposal, made on Monday, offered US$5.21 a share for Santos, and was contingent on the Australian company hedging some of its future...